CN1321266C

CN1321266C - Rotor blade of diagonal flow water turbine

Info

Publication number: CN1321266C
Application number: CNB2004100815155A
Authority: CN
Inventors: 张礼达; 余波; 陈冬冬
Original assignee: Xihua University
Current assignee: Xihua University
Priority date: 2004-12-17
Filing date: 2004-12-17
Publication date: 2007-06-13
Anticipated expiration: 2024-12-17
Also published as: CN1621682A

Abstract

The invention relates to a runner blade of a diagonal flow water turbine. A reasonable flow model is established for the blade, and the model and basic equations (1), (6), (12) and (14) are used to form a flow surface based on S ₁ The main equation of the quasi-three-dimensional inverse problem calculation, according to these basic equations design and calculation to obtain the basic data, based on these basic data to manufacture the oblique flow turbine runner blades, with good energy and cavitation performance, the number of runner blades 5-6 pieces, used in 30-70 meters of water head, to fill the economic and technical deficiencies in the water head section (30-70 meters) of the mixed flow and axial loss turbine.

Description

Diagonal Flow Turbine Runner Blades

技术领域：Technical field:

本发明涉及一种斜流式水轮机转轮叶片，属于流体机械领域。The invention relates to a runner blade of a diagonal flow water turbine, which belongs to the field of fluid machinery.

背景技术：Background technique:

水轮机是水电站的专用动力机械，水电站的装机容量约占全国总装机容量的25％，因此，水轮机的性能直接关系到水电站的出力和寿命。水轮机主要型式有轴流式、混流式、贯流式、冲击式等，斜流式水轮机是介于轴流式和混流式之间的一种机型。在专利文献数据库中，如专利号为：ZL97195388.0的《弗朗西斯水轮机的叶轮》只提出了结构形状，而未提出水轮机转叶轮的设计计算数学方程表达式，因而不能建立水力模型。Hydro turbines are special power machinery for hydropower stations. The installed capacity of hydropower stations accounts for about 25% of the total installed capacity of the country. Therefore, the performance of hydroturbines is directly related to the output and life of hydropower stations. The main types of water turbines are axial flow type, mixed flow type, tubular flow type, impact type, etc. Diagonal flow type turbine is a model between axial flow type and mixed flow type. In the patent literature database, for example, the patent number: ZL97195388.0 "Impeller of Francis Water Turbine" only proposes the structural shape, but does not propose the mathematical equation expression for the design and calculation of the impeller of the water turbine, so the hydraulic model cannot be established.

在公开发表的斜流式水轮机设计理论及方法中如：(Bankhend水电站转轮更换方案的设计研究/(加拿大)HungD；尹继红//《国外大电机》.-2001(4).-77-81)，只讲述了斜流式水轮机转轮更换方案以及对既有转轮进行改型设计的三维计算程序，和本发明所涉及的利用两个相对流面理论，根据斜流式水轮机转轮具体的流道参数，建立流动方程，通过两个流面迭代计算的准三元计算不同。Among the publicly published design theories and methods of oblique flow turbines, such as: (Design Research on the Runner Replacement Scheme of Bankhend Hydropower Station/(Canada) HungD; Yin Jihong//"Foreign Large Electric Machines".-2001(4).-77-81 ), only described the replacement scheme of the oblique flow turbine runner and the three-dimensional calculation program for the retrofit design of the existing runner, and the use of two relative flow surface theories involved in the present invention, according to the specific The parameters of the flow path, the establishment of the flow equation, and the quasi-ternary calculation through the iterative calculation of the two flow surfaces are different.

又如(高水头大容量变转速斜流式水泵水轮机的研制/宫川数吉//《国外大电机》.-1999(2).-47-51)，该文采用几种数字流动分析方法设计了斜流式水泵水轮机，其工作水头和输入/输出功率为常规机组的两倍，并进行了相应的模型试验。介绍了该种水泵水轮机的模型试验结果，从水动力学和结构强度的观点出发，确定固定导叶和活动导叶分别为24，转轮叶片数为10，本发明的主要内容是斜流式水轮机转轮叶片，设计水头段在30-70米之间，叶片数为5或6片，从结构型式以及实用范围的角度都不同。Another example (Development of High Head, Large Capacity, Variable Speed Diagonal Flow Pump Turbine/Miyagawa Shukichi//"Foreign Large Electric Machines".-1999(2).-47-51), this article uses several digital flow analysis methods A diagonal-flow pump-turbine was designed, whose working head and input/output power were twice those of conventional units, and corresponding model tests were carried out. The model test results of this kind of water pump turbine are introduced. From the viewpoint of hydrodynamics and structural strength, it is determined that the number of fixed guide vanes and movable guide vanes is 24, and the number of runner blades is 10. The main content of the invention is the oblique flow type. The turbine runner blades are designed to have a water head between 30 and 70 meters, and the number of blades is 5 or 6, which are different from the perspective of structural type and practical range.

再如(斜流式水泵水轮机工况零流量制动力矩的计算/于治明//《沈阳航空工业学院学报》.-2000，17(3).-81-83)，该文利用πo-型式斜流式水泵水轮机的模型静态全特性曲线，分析了影响泵工况零流量制动力矩的主要因素，推导出了斜流式水泵工况零流量制动力矩的计算公式。适用于斜流式水泵水轮机机组的主阀关闭，导叶，轮叶以一定规律开启时，泵工况起动过渡的计算，也不涉及水轮机转轮叶片的范畴。Another example (Calculation of Zero Flow Braking Moment of Diagonal Flow Pump Turbine Working Condition/Yu Zhiming//"Journal of Shenyang Aeronautical Industry Institute".-2000, 17(3).-81-83), this paper uses πo- The static full characteristic curve of the model of the diagonal flow pump-turbine is analyzed, the main factors affecting the zero flow braking torque of the pump working condition are analyzed, and the calculation formula of the zero flow braking torque of the diagonal flow pump working condition is deduced. It is suitable for the calculation of the start-up transition of the pump when the main valve of the diagonal flow pump turbine unit is closed, the guide vane and the vane are opened in a certain order, and it does not involve the scope of the turbine runner blade.

再又如(全电动中小容量斜流式水轮机的系列化/彭泽元//《水电站机电技术》.-1994，7(3).-65-67)，介绍了日本三菱重工与中部电力公司共同研究开发的中小容量斜流转桨式水轮机叶片操作电动接力器，通过制作样机进行验证试验，完成了全电动中小容量斜流式水轮机的系列化，其主要内容在于叶片操作控制机构，和本发明的斜流式水轮机转轮及叶片设计相比，属于不同的技术领域。Another example (Serialization of all-electric small and medium-capacity oblique flow turbines/Peng Zeyuan//"Electromechanical Technology of Hydropower Stations".-1994, 7(3).-65-67), introduced the joint research of Japan's Mitsubishi Heavy Industries and Chubu Electric Power Company The developed small and medium-capacity oblique-flow paddle turbine blade-operated electric servomotor has completed the serialization of all-electric medium and small-capacity oblique-flow turbines through the production of a prototype. Compared with flow turbine runner and blade design, it belongs to different technical fields.

发明内容：Invention content:

本发明的目的是依据水流实际流动状态，提出新的斜流式水轮机的设计方法，根据两类相对流面(S₁，S₂)的流动理论和斜流式水轮机转轮具体的流道参数，建立两个流面的流动方程，通过两个流面迭代计算的准三元计算设计。设计出新型的斜流式转轮叶片，使之具有合理形状的转轮，供水电站选择，提高斜流式水轮机的效率和抗气蚀能力。The purpose of the present invention is to propose a new design method for a diagonal flow turbine based on the actual flow state of the water flow, based on the flow theory of two types of relative flow surfaces (S ₁ , S ₂ ) and the specific flow path parameters of the runner of the diagonal flow turbine , establish the flow equations of two flow surfaces, and design through the quasi-ternary calculation of iterative calculation of two flow surfaces. Design a new type of oblique flow runner blade, so that it has a reasonable shape of the runner, which is selected for the hydropower station and improves the efficiency and anti-cavitation ability of the oblique flow turbine.

本发明的设计方法基于准三维反问题计算以S₁流面和S_2m流面计算为基础，其特征在于提出如下流动模型，其设计基本方程式为：The design method of the present invention is based on the calculation of the quasi-three-dimensional inverse problem based on the calculation of the S ₁ flow surface and the S _2m flow surface, and is characterized in that the following flow model is proposed, and its basic design equation is:

$\frac{&PartialD; &PartialD;}{&PartialD; &PartialD; r r} ((\frac{11}{r r {B B}_{f f}} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; r r})) + + \frac{&PartialD; &PartialD;}{&PartialD; &PartialD; z z} ((\frac{11}{{rB rB}_{f f}} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; z z})) = = \frac{11}{r r} ((tgμ tgμ \frac{{&PartialD; &PartialD; V V}_{θ θ} r r}{&PartialD; &PartialD; r r} - - tgλ tgλ \frac{{&PartialD; &PartialD; V V}_{θ θ} r r}{&PartialD; &PartialD; z z}))$

$+ + \frac{11}{{W W}^{22}} [[\frac{&PartialD; &PartialD; E E.}{&PartialD; &PartialD; r r} (({W W}_{z z} - - {W W}_{θ θ} tgμ tgμ)) - - \frac{&PartialD; &PartialD; E E.}{&PartialD; &PartialD; z z} (({W W}_{r r} - - {W W}_{θ θ} tgλ tgλ))]] - - - - - - ((11))$

$\frac{&PartialD; &PartialD;}{&PartialD; &PartialD; m m} ((\frac{r r}{h h} \frac{&PartialD; &PartialD; Ψ Ψ}{&PartialD; &PartialD; m m})) + + \frac{&PartialD; &PartialD;}{&PartialD; &PartialD; θ θ} ((\frac{11}{hr hr} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; θ θ})) = = 22 ωr ωr \frac{&PartialD; &PartialD; r r}{&PartialD; &PartialD; m m} = = 22 sin sin σ σ - - - - - - ((66))$

dX/dm＝R^*/R，dY/dθ＝-R^* (14)dX/dm=R ^* /R, dY/dθ=-R ^* (14)

上述公式中符号见下面具体实施例中说明。The symbols in the above formulas are described in the following specific examples.

所述的斜流式水轮机转轮叶片的安装角在进水边为22.97°-31.80°之间，出水边为22.56°-30.64°。The installation angle of the runner blades of the oblique flow turbine is between 22.97°-31.80° on the water inlet side and 22.56°-30.64° on the water outlet side.

所述的斜流式水轮机转轮叶片数为5片或6片。The number of runner blades of the oblique flow turbine is 5 or 6.

附图说明：Description of drawings:

结合附图对本发明做进一步说明The present invention will be further described in conjunction with accompanying drawing

图1 转轮流道示意图Figure 1 Schematic diagram of runner flow path

图2 等价速度三角形Figure 2 Equivalent velocity triangle

图3A S₁流面叶型展开图(5个断面)Figure 3A S ₁ flow surface airfoil expansion diagram (5 sections)

图3B，3C 叶片三维图Figure 3B, 3C three-dimensional view of the blade

图4A 斜流式转轮结构正视图Figure 4A Front view of the oblique flow runner structure

图4B 斜流式转轮结构剖面图Figure 4B Structural cross-sectional view of the oblique flow runner

图4C 斜流式转轮叶片安装Figure 4C Diagonal flow runner blade installation

图4D 斜流式转轮叶片安装孔Figure 4D Diagonal Flow Runner Blade Mounting Hole

图5A 5叶片转轮实物图Figure 5A 5-blade runner physical picture

图5B6叶片转轮实物图Figure 5B6 The physical picture of the blade runner

1斜流式转轮叶片型线 2斜流式转轮叶片把合螺栓1 Diagonal flow runner blade profile 2 Diagonal flow runner blade binding bolts

3斜流式转轮体 4键槽 5叶片定位销孔3 oblique flow runner body 4 key groove 5 blade positioning pin hole

具体实施方式：Detailed ways:

如图1、图2所示用方程(1)、(6)、(12)、(14)构成了基于S₁流面的准三维反问题计算的主方程，通过S_2m流面计算给定初始叶型的S₁流面反问题与平均S_2m流面正问题迭代，并在回转面(S₁相对流面)引入“等价速度三角形”，用轴向速度变化率ξ和流面倾斜参数η来修正因流面倾斜和轴向速度变化而引起叶栅性能变化的影响，设计斜流式转轮叶片。进行轴面流动计算得到轴面流动后，就可得到若干回转S₁面，然后在回转S₁流面上设计出叶片形状，最后将这些叶片按公式

积分形成三维实体叶片，并按公式加厚。其叶片安装角在进水边为22.97″-31.80″之间，出水边为22.56″-30.64″。叶片数为5片或6片。As shown in Fig. 1 and Fig. 2, equations (1), (6), (12), and (14) constitute the main equation for the calculation of the quasi-three-dimensional inverse problem based on the S ₁ flow surface, which is given by the calculation of the S _2m flow surface The inverse problem of the S ₁ flow surface of the initial airfoil and the forward problem of the average S _2m flow surface are iterated, and the "equivalent velocity triangle" is introduced on the turning surface (S ₁ relative flow surface), and the axial velocity change rate ξ and the flow surface inclination The parameter η is used to correct the influence of the performance change of the cascade caused by the inclination of the flow surface and the change of the axial velocity, and the oblique flow runner blade is designed. After calculating the flow on the axial surface and obtaining the flow on the axial surface, several rotating S ₁ surfaces can be obtained, and then the blade shape is designed on the rotating S ₁ flow surface, and finally these blades are calculated according to the formula

Integral to form a three-dimensional solid blade, and according to the formula thickened. The blade installation angle is between 22.97″-31.80″ at the water inlet side, and 22.56″-30.64″ at the water outlet side. The number of leaves is 5 or 6.

设计计算的基本过程：The basic process of design calculation:

1基于S₁流面的准三维反问题计算数学模型1 Computational mathematical model of quasi-3D inverse problem based on S ₁ flow surface

(1)平均S_2m流面流动控制方程(1) Average S _2m surface flow governing equation

假设转轮内部相对流动定常，水流无粘性不可压，对转轮内实际三维流动进行周向平均处理，可得转轮区周向平均的流函数控制方程：Assuming that the relative flow inside the runner is constant, and the water flow is inviscid and incompressible, and the actual three-dimensional flow in the runner is averaged in the circumferential direction, the governing equation of the circumferentially averaged flow function in the runner area can be obtained:

$\frac{&PartialD; &PartialD;}{&PartialD; &PartialD; r r} ((\frac{11}{{rB rB}_{f f}} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; r r})) + + \frac{&PartialD; &PartialD;}{&PartialD; &PartialD; z z} ((\frac{11}{{rB rB}_{f f}} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; z z})) = = \frac{11}{r r} ((tgμ tgμ \frac{{&PartialD; &PartialD; V V}_{θ θ} r r}{&PartialD; &PartialD; r r} - - tgλ tgλ \frac{{&PartialD; &PartialD; V V}_{θ θ} r r}{&PartialD; &PartialD; z z}))$

$+ + \frac{11}{{W W}^{22}} [[\frac{&PartialD; &PartialD; E E.}{&PartialD; &PartialD; r r} (({W W}_{z z} - - {W W}_{θ θ} tgμ tgμ)) - - \frac{&PartialD; &PartialD; E E.}{&PartialD; &PartialD; z z} (({W W}_{r r} - - {W W}_{θ θ} tgλ tgλ)) - - - - - - ((11))$

平均流动函数定义为：The average flow function is defined as:

$\frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; r r} = = {rB rB}_{f f} \overset{&OverBar; &OverBar;}{{W W}_{22}},, \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; z z} = = - - {rB rB}_{f f} \overset{&OverBar; &OverBar;}{{W W}_{r r}} - - - - - - ((22))$

式中： $B_{f} = \frac{B \cdot Δθ}{2 π}$ In the formula: $B_{f} = \frac{B \cdot Δθ}{2 π}$

对于轴面有势流动，tgλ和tgμ为0，E为常数，因此，方程(1)的右端项为0。For the potential flow on the axial surface, tgλ and tgμ are 0, and E is a constant, so the right-hand term of equation (1) is 0.

(2)S₁相对流面流动控制方程(2) S ₁ relative flow governing equation

S₁回转相对流面上的连续方程为：The continuity equation on the relative flow surface of S ₁ revolution is:

$\frac{&PartialD; &PartialD;}{&PartialD; &PartialD; m m} (({hrW wxya}_{m m})) + + \frac{&PartialD; &PartialD;}{&PartialD; &PartialD; θ θ} (({hW wxya}_{θ θ})) = = 00 - - - - - - ((33))$

S₁流面的运动方程为：The motion equation of S ₁ flow surface is:

$\frac{&PartialD; &PartialD; (({rW wxya}_{00}))}{&PartialD; &PartialD; m m} - - \frac{{&PartialD; &PartialD; W W}_{m m}}{&PartialD; &PartialD; θ θ} = = \frac{&PartialD; &PartialD;}{&PartialD; &PartialD; m m} (({k k}_{m m} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; m m})) + + \frac{&PartialD; &PartialD;}{&PartialD; &PartialD; θ θ} (({k k}_{θ θ} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; θ θ})) - - - - - - ((44))$

$= = 22 ωr ωr \frac{&PartialD; &PartialD; r r}{&PartialD; &PartialD; m m} = = 22 ω ω r r sin sin σ σ + + \frac{h h}{{W W}^{22}} ((\frac{&PartialD; &PartialD; E E.}{r r &PartialD; &PartialD; θ θ} {W W}_{m m} - - \frac{&PartialD; &PartialD; E E.}{&PartialD; &PartialD; m m} {W W}_{θ θ}))$

式中： $k_{m} = \frac{r}{h}, k_{θ} = \frac{1}{hr}$ In the formula: $k_{m} = \frac{r}{h}, k_{θ} = \frac{1}{hr}$

h——S₁流面的流层厚度；h——flow layer thickness of S ₁ flow surface;

m——子午面座标。m—coordinate of meridian plane.

方程(3)和(4)构成了S₁相对流面绝对无旋运动的基本方程组。Equations (3) and (4) constitute the basic equations for the absolute irrotational motion of S ₁ relative to the flow surface.

根据连续方程(3)定义流函数为：According to the continuity equation (3), the flow function is defined as:

$\frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; θ θ} = = {rhW wxya}_{m m},, \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; m m} = = - - {hW wxya}_{00} - - - - - - ((55))$

代入方程(4)，可得出S₁流面相对运动的流函数方程：Substituting into equation (4), the flow function equation of the relative motion of the flow surface of S ₁ can be obtained:

(3)基于S₁流面的叶型设计(3) Airfoil design based on S ₁ flow surface

叶片方程如下：The blade equation is as follows:

对于S₁流面流动，定义如下周向平均：For S ₁ stream surface flow, the circumferential average is defined as follows:

$\overset{&OverBar; &OverBar;}{q q} ((m m)) = = \frac{11}{{θ θ}_{p p} - - {θ θ}_{s the s}} {&Integral; &Integral;}_{{θ θ}_{s the s}}^{{θ θ}_{p p}} q q ((m m,, θ θ)) dθ dθ - - - - - - ((88))$

将式(8)引入式(7)可得基于S₁流面计算的叶片积分方程Introducing Equation (8) into Equation (7), the blade integral equation calculated based on the S ₁ flow surface can be obtained

式中： $\overset{&OverBar;}{V_{θ}} (m) = \frac{1}{θ_{p} - θ_{s}} {&Integral;}_{θ_{x}}^{θ_{p}} V_{θ} (m, θ) dθ,$ In the formula: $\overset{&OverBar;}{V_{θ}} (m) = \frac{1}{θ_{p} - θ_{the s}} {&Integral;}_{θ_{x}}^{θ_{p}} V_{θ} (m, θ) dθ,$

$\overset{&OverBar; &OverBar;}{{W W}_{θ θ}} ((m m)) = = \frac{11}{{θ θ}_{p p} - - {θ θ}_{s the s}} {&Integral; &Integral;}_{{θ θ}_{x x}}^{{θ θ}_{p p}} {W W}_{θ θ} ((m m,, θ θ)) dθ dθ$

一阶常微分方程(9)求解需给定初值条件。称此条件为叶片叠加条件，对斜流式水轮机转轮，取Z_st为叶片旋转轴的轴向坐标，给定如下初值条件：To solve the first-order ordinary differential equation (9), the initial value condition must be given. This condition is called the blade superposition condition. For the runner of the diagonal flow turbine, Z _st is taken as the axial coordinate of the blade rotation axis, and the following initial value conditions are given:

(r，z＝z_st)＝0 (10)(r,z=z _st )=0 (10)

初始叶型与最终设计叶型间修正公式：Correction formula between initial airfoil shape and final design airfoil shape:

由于与⁽ⁿ⁾间为非线性关系，故采用松弛迭代，叶型修正可写为：because and  ⁽ⁿ⁾ is a nonlinear relationship, so using relaxation iteration, leaf shape correction can be written as:

这样，基于给定初始叶型，通过S_2m流面流动和S₁流面流动计算，采用式(11)进行叶型迭代修正，并使之满足叶片叠加条件，实现了S₁流面上的叶型设计。In this way, based on the given initial blade shape, through the calculation of S _2m flow surface flow and S ₁ flow surface flow, formula (11) is used to iteratively correct the blade shape, and make it meet the superposition conditions of blades, and realize the S ₁ flow surface leaf design.

给定叶片向厚度t_n(r，z，θ)，考虑叶片的三维扭曲，叶片的周向厚度t_n(r，z，θ)则由下式给出：Given the blade thickness t _n (r, z, θ), considering the three-dimensional distortion of the blade, the circumferential thickness t _n (r, z, θ) of the blade is given by the following formula:

基于所设计的叶片中面，由式(13)求得厚度t_s进行背面加厚，则可得到设计厚度的叶片，实现转轮的准三维设计。Based on the designed mid-surface of the blade, the thickness t _s obtained from formula (13) is thickened on the back side, and the blade with the designed thickness can be obtained, realizing the quasi-three-dimensional design of the runner.

2任意倾斜回转流面的变换2 Transformation of any inclined swirling flow surface

(1)任意倾斜回转面的基本方程(1) The basic equation of any inclined surface of revolution

连续方程：Continuity equation:

$\frac{&PartialD; &PartialD;}{&PartialD; &PartialD; m m} ((hr hr {W W}_{m m})) + + \frac{&PartialD; &PartialD;}{&PartialD; &PartialD; θ θ} (({hW wxya}_{θ θ})) = = 00$

流函数ψ的方程：Equation for the stream function ψ:

$\frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; θ θ} = = {rhW wxya}_{m m},, \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; m m} = = - - {hW wxya}_{00}$

满足于流函数ψ的回转流面相对运动方程：The relative motion equation of the rotary flow surface satisfying the flow function ψ:

$\frac{{&PartialD; &PartialD;}^{22} ψ ψ}{{&PartialD; &PartialD; m m}^{22}} + + \frac{11}{{r r}^{22}} \frac{{&PartialD; &PartialD;}^{22} ψ ψ}{{&PartialD; &PartialD; θ θ}^{22}} + + [[\frac{11}{r r} \frac{&PartialD; &PartialD; r r}{&PartialD; &PartialD; m m} - - \frac{11}{h h} \frac{&PartialD; &PartialD; ((h h))}{&PartialD; &PartialD; m m}]] \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; m m} - - \frac{11}{h h} \frac{&PartialD; &PartialD; ((h h))}{r r &PartialD; &PartialD; θ θ} = = 22 ωh ωh \frac{&PartialD; &PartialD; r r}{&PartialD; &PartialD; m m}$

(2)等价速度三角形理论(2) Equivalent Velocity Triangle Theory

将倾斜的回转流面在任定基准半径R^*的圆柱面的展开面x-y面内映象。引入映象函数Map the inclined swirling flow surface in the xy plane of the expansion surface of the cylindrical surface with an arbitrary reference radius R ^* . import mapping function

dX/dm＝R^*/R， dY/dθ＝-R^* (14)dX/dm=R ^* /R, dY/dθ=-R ^* (14)

由于叶栅进、出口的轴向速度不等，因此引进“等价速度三角形”如图2所示。Since the axial velocity of the inlet and outlet of the cascade is not equal, an "equivalent velocity triangle" is introduced, as shown in Figure 2.

因流面倾斜和轴向速度变化而引起叶栅性能变化的影响，分别用轴向速度变化率ξ和流面倾斜参数η来反映：The influence of the cascade performance change caused by the inclination of the flow surface and the change of the axial velocity is reflected by the axial velocity change rate ξ and the flow surface inclination parameter η respectively:

$ξ ξ = = \frac{{W W}_{X x 22} - - {W W}_{X x 22}}{{W W}_{X x \infty \infty}} - - - - - - ((1515))$

$η η = = \frac{{22 u u}^{* *}}{{W W}_{X x 11} + + {W W}_{X x 22}} ((\frac{{R R}_{11}^{22} - - {R R}_{22}^{22}}{{R R}^{* * 22}})) - - - - - - ((1616))$

最后，通过式(14)将叶栅转换到物理面上。Finally, the cascade is converted to the physical plane by formula (14).

3两类流面准三元迭代3 Quasi-ternary iteration of two types of flow surfaces

方程(1)、(6)、(12)、(14)构成了基于S₁流面的准三维反问题计算的主方程，分别如下：Equations (1), (6), (12), and (14) constitute the main equations for the calculation of the quasi-three-dimensional inverse problem based on the S ₁ flow surface, which are as follows:

$\frac{&PartialD; &PartialD;}{&PartialD; &PartialD; r r} ((\frac{11}{{rB rB}_{f f}} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; r r})) + + \frac{&PartialD; &PartialD;}{&PartialD; &PartialD; z z} ((\frac{11}{{rB rB}_{f f}} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; z z})) = = \frac{11}{r r} ((tgμ tgμ \frac{{&PartialD; &PartialD; V V}_{θ θ} r r}{&PartialD; &PartialD; r r} - - tgλ tgλ \frac{{&PartialD; &PartialD; V V}_{θ θ} r r}{&PartialD; &PartialD; z z})) - - - - - - ((11))$

$+ + \frac{11}{{W W}^{22}} [[\frac{&PartialD; &PartialD; E E.}{&PartialD; &PartialD; r r} (({W W}_{z z} - - {W W}_{θ θ} tgμ tgμ)) - - \frac{&PartialD; &PartialD; E E.}{&PartialD; &PartialD; z z} (({W W}_{r r} - - {W W}_{θ θ} tgλ tgλ))]]$

dX/dm＝R^*/R，dY/dθ＝-R^* (14)dX/dm=R ^* /R, dY/dθ=-R ^* (14)

对方程(1)和方程(6)分别建立有限元方程并进行迭代计算，在S₁流面计算时，用方程(14)转化到映像面，引入“等价速度三角形”，用轴向速度变化率ξ和流面倾斜参数η来修正因流面倾斜和轴向速度变化而引起叶栅性能变化的影响，再用(14)转化回物理面，继续迭代，直至满足收敛条件。Establish finite element equations for Equation (1) and Equation (6) respectively and perform iterative calculations. When calculating the S ₁ flow surface, use Equation (14) to convert to the image surface, introduce the "equivalent velocity triangle", and use the axial velocity The change rate ξ and the flow surface inclination parameter η are used to correct the influence of the cascade performance change caused by the flow surface inclination and axial velocity changes, and then use (14) to convert back to the physical surface, and continue to iterate until the convergence condition is met.

本发明的优点是：The advantages of the present invention are:

通过对斜流式水轮机的研究，采用系统设计，综合考虑水轮机性能指标与几何参数各特性间的影响，应用斜流式水轮机的设计方法和优化理论，建立数学模型，利用准三元理论，通过对S₁/S₂流面进行迭代计算，设计出了具有良好水力性能的斜流式水轮机转轮。该斜流式水轮机改善了轴流式水轮机高水头(30米以上)与混流式水轮机低水头(30-70米)段之间水流能量转换效率低，变负荷运行时效率低，空蚀破坏严重，电站经济效益差等缺陷，使该水头段(30-70米)现有水电站增容技改或新建电站的性价比得到较大提高。Through the research on the diagonal flow turbine, the system design is adopted, the influence between the performance index and the geometric parameters of the turbine is comprehensively considered, and the design method and optimization theory of the diagonal flow turbine are used to establish a mathematical model. Using the quasi-ternary theory, through Through iterative calculation of S ₁ /S ₂ flow surface, a diagonal flow turbine runner with good hydraulic performance is designed. The oblique flow turbine improves the low efficiency of water flow energy conversion between the high head (above 30 meters) of the axial flow turbine and the low head (30-70 meters) of the mixed flow turbine, low efficiency during variable load operation, and serious cavitation damage , Poor economic benefits of the power station and other defects have greatly improved the cost performance of the existing hydropower station (30-70 meters) in the water head section (30-70 meters) for capacity expansion and technical transformation or new power stations.

Claims

1, a kind of oblique flow water turbine runner blade is characterized in that following flow model is proposed, and its basic design equation is:

\frac{&PartialD; &PartialD;}{&PartialD; &PartialD; r r} ((\frac{11}{r r {B B}_{f f}} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; r r})) + + \frac{&PartialD; &PartialD;}{&PartialD; &PartialD; z z} ((\frac{11}{r r {B B}_{f f}} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; z z})) = = \frac{11}{r r} ((tgμ tgμ \frac{&PartialD; &PartialD; {V V}_{θ θ} r r}{&PartialD; &PartialD; r r} - - tgλ tgλ \frac{&PartialD; &PartialD; {V V}_{θ θ} r r}{&PartialD; &PartialD; z z}))

+ + \frac{11}{{W W}^{22}} [[\frac{&PartialD; &PartialD; E E.}{&PartialD; &PartialD; r r} (({W W}_{Z Z} - - {W W}_{θ θ} tgμ tgμ)) - - \frac{&PartialD; &PartialD; E E.}{&PartialD; &PartialD; z z} (({W W}_{r r} - - {W W}_{θ θ} thλ thλ))]] - - - - - - ((11))

This equation is the governing equation of the flow function averaged in the circumferential direction of the runner area. In the formula: z, r, θ are the cylindrical coordinate system, W is the relative velocity, W _r is the component of the relative velocity along the radial direction, and W _θ is the relative velocity along the Circumferential component, W _z is the component of relative velocity along the axial direction; E is the energy per unit mass of fluid in relative motion;

B_{f} = \frac{BΔθ}{2 π};

ψ is the flow function; tgλ and tgμ describe the geometric characteristics of the flow surface, given by

tgλ = \frac{{no}_{r}}{{no}_{θ}},

tgμ = \frac{{no}_{z}}{{no}_{θ}}

Determine, n _r , n _θ , n _z represent the radial, circumferential and axial unit vectors of the flow surface, respectively;

\frac{&PartialD; &PartialD;}{&PartialD; &PartialD; m m} ((\frac{r r}{h h} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; m m})) + + \frac{&PartialD; &PartialD;}{&PartialD; &PartialD; θ θ} ((\frac{11}{hr hr} \frac{&PartialD; &PartialD; ψ ψ}{&PartialD; &PartialD; θ θ})) = = 22 ωr ωr \frac{&PartialD; &PartialD; r r}{&PartialD; &PartialD; m m} = = 22 ω ω r r sin sin σ σ - - - - - - ((66))

This equation is the flow function equation of the relative motion of the _S1 flow surface, where: r is the radius of the calculated streamline, m is the coordinate of the meridional surface, h is the flow layer thickness of the _S1 flow surface, ω is the angular velocity,

\sin σ = \frac{&PartialD; r}{&PartialD; m}

is the geometry parameter about the S ₁ flow surface, given by calculating the average S _2m flow surface flow;

This equation is the airfoil correction equation, where: r _c is the calculated average runner radius, r _g is the given average radius, and n is the number of iterations;

dX/dm=R ^* /R, dY/dθ=-R ^* (14)

The equation is a mapping function equation, where: X, Y are the tilted swirling flow surface at any reference radius

The xy coordinates on the cylindrical expansion surface of R ^* , R is the radius of the inclined gyratory flow surface.

2. The runner blade of a diagonal flow turbine according to claim 1, wherein the installation angle of the runner blade is between 22.97°-31.80° at the water inlet side and 22.56°-30.64° at the water outlet side.

3. The runner blade of the diagonal flow turbine according to claim 1, wherein the number of runner blades is 5 or 6.